Final answer:
To solve for x, set up an equation with the given angles and solve for x.
Step-by-step explanation:
To solve for x, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
We have two known angles: (8x-9)° and 63°.
We can set up an equation: (8x-9) + 63 + x = 180
Simplifying the equation, we have: 9x + 54 = 180
Subtracting 54 from both sides, we get: 9x = 126
Finally, dividing both sides by 9, we find that x = 14.